Exact Simulation of Hawkes Process with Exponentially Decaying Intensity

Electronic Communications in Probability, Vol. 18, No. 62, 2013

15 Pages Posted: 18 Jul 2013

See all articles by Angelos Dassios

Angelos Dassios

London School of Economics & Political Science (LSE) - Department of Statistics

Hongbiao Zhao

Shanghai University of Finance and Economics; London School of Economics & Political Science (LSE)

Date Written: July 17, 2013

Abstract

We introduce a numerically efficient simulation algorithm for Hawkes process with exponentially decaying intensity, a special case of general Hawkes process that is most widely implemented in practice. This computational method is able to exactly generate the point process and intensity process, by sampling interarrival-times directly via the underlying analytic distribution functions without numerical inverse, and hence avoids simulating intensity paths and introducing discretisation bias. Moreover, it is flexible to generate points with either stationary or non-stationary intensity, starting from any arbitrary time with any arbitrary initial intensity. It is also straightforward to implement, and can easily extend to multi-dimensional versions, for further applications in modelling contagion risk or clustering arrival of events in finance, insurance, economics and many other fields. Simulation algorithms for one dimension and multi-dimension are represented, with numerical examples of univariate and bivariate processes provided as illustrations.

Keywords: Contagion risk, Stochastic intensity model, Self-exciting point process, Hawkes process, Hawkes process with exponentially decaying intensity, Exact simulation, Monte Carlo simulation

JEL Classification: C15, C53, C63

Suggested Citation

Dassios, Angelos and Zhao, Hongbiao, Exact Simulation of Hawkes Process with Exponentially Decaying Intensity (July 17, 2013). Electronic Communications in Probability, Vol. 18, No. 62, 2013, Available at SSRN: https://ssrn.com/abstract=2295068

Angelos Dassios

London School of Economics & Political Science (LSE) - Department of Statistics ( email )

Houghton Street
London, England WC2A 2AE
United Kingdom

Hongbiao Zhao (Contact Author)

Shanghai University of Finance and Economics ( email )

No. 777 Guoding Road
Yangpu District
Shanghai, Shanghai 200433
China

HOME PAGE: http://hongbiaozhao.weebly.com/

London School of Economics & Political Science (LSE)

Houghton Street
London, WC2A 2AE
United Kingdom

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